| Robert Heath - 1760 - 412 sider
...Radius : Dif. Long, nearly. J Ltt. : Dif. Longitude. J Mid. Lat. : Dif. Longitude. SINCE the Produft **of the two Extremes is equal to the Product of the two** middle Terms, in any Proportion, therefore fubftituting in the 5th Proportion Difl. run X Sine Courfe... | |
| John Hill - 1765 - 416 sider
...96 by 24 ; all being. terms equally diftant. THEOREM IV. In any geometrical progreffion whatfoever, **the product of the two extremes is equal to the product of** any other two immediate terms of like diftance from both. EXAMPLE. 5, 20, 80, 320, 1280, 5120. So in... | |
| Alexander Ewing - 1799 - 328 sider
...antecedents-, and the feconct and fourth terms, 32 and 24, are confequents. In four proportional numbers, **the product of the two extremes is- equal to the product of -the two means** ; End. B. 6 prop. 16. ; thus^ if -1€ s• 3* • 1 12 ! 24, then 16X24=32X 12 = 384. When four quantities-are... | |
| Jeremiah Paul - 1801 - 222 sider
...27, 9,3, 1, decrease by the common divisor 3. In any series of numbers, in Geometrical Progression, **the product of the two extremes, is equal to the product of** any two means, equally distant therefrom ; or of the product of the middle term by itself: Thus, 1,... | |
| Tiberius Cavallo - 1803
...multiplied by AS. Then D is the centre of percuflion. And fmce, when four quantities are proportional, **the product of the two extremes is equal to the product of the two means;** therefore if the weight of A multiplied by AS, be again multiplied by AD, the product muft be equal... | |
| Charles Hutton - 1811
...multiplication for addition, &c, , - 1. When 1. Wh.en four quantities are in geometrical proportion, **the product of the two extremes is equal to the product of the two means.** As in these, 3, 6, 4, 8, where 3x8=6 X 4 = 24; and in these, a, ar, b, br, where ax. br = ar x i, z:... | |
| Charles Hutton - 1812
...and reason of the practice in the Rule of Three. THEOREM 2. In any continued geometrical progression, **the product of the two extremes is equal to the product of** any two means that are equally distant from them, or equal to the square of the middle term when there... | |
| John Gough - 1813 - 348 sider
...be equal to the product of the extremes. Proposition Proposition 3. In any geometrical progression **the product of the two extremes, is equal to the product of** any two terms equally distant from the two extremes. 3, 6, 12, 24, 48, 96, 3, 6, 12, 24, 48, 9/5, 102,... | |
| John Bonnycastle - 1813
...• — • • » 2 ' 6 ' ' 3 • 9' a • b • ' с • d 9. In any continued geometrical series, **the product of the two extremes is equal to the product of** any two means that are equally distant from them ; or to the square of the mean, when the number of... | |
| Jeremiah Day - 1814 - 303 sider
...section, so far as to admit the principle, that " when four quantities are in geometrical proportion, **the product of the two extremes is equal to the product of the two means** :" a principle which is at the foundation of the Rule of Three in arithmetic. See Webber's Arithmetic.... | |
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